Question: In right triangle $XYZ$ with $\angle YXZ = 90^\circ$, we have $XY = 24$ and $YZ = 25$.  Find $\tan Y$.
Answer: [asy]

pair X,Y,Z;

X = (0,0);

Y = (24,0);

Z = (0,7);

draw(X--Y--Z--X);

draw(rightanglemark(Y,X,Z,23));

label("$X$",X,SW);

label("$Y$",Y,SE);

label("$Z$",Z,N);

label("$25$",(Y+Z)/2,NE);

label("$24$",Y/2,S);

[/asy]

The Pythagorean Theorem gives us $XZ= \sqrt{YZ^2 - XY^2} = \sqrt{625-576} = \sqrt{49}=7$, so $\tan Y = \frac{XZ}{XY} = \ \boxed{\frac{7}{24}}$.